Golf ball dimple profile

ABSTRACT

Golf ball dimples having a cross-sectional profile shape partially defined by a Gabriel&#39;s Horn curve are disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent application Ser. No. 13/341,717, filed Dec. 30, 2011, the entire disclosure of which is hereby incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to a golf ball dimple cross-sectional profile a portion of which is defined by a Gabriel's Horn curve.

BACKGROUND OF THE INVENTION

Golf ball dimples are known to have a significant effect on the aerodynamic forces acting on the ball during flight. For example, the dimples on a golf ball create a turbulent boundary layer around the ball. The turbulence energizes the boundary layer and helps it stay attached further around the ball to reduce the area of the wake. This greatly increases the pressure behind the ball and substantially reduces the drag. Based on the role that dimples play in reducing drag, golf ball manufacturers continually seek to develop novel dimple patterns, sizes, shapes, volumes, cross-sections, etc., in order to optimize flight performance.

SUMMARY OF THE INVENTION

In a particular embodiment, the present invention is directed to a golf ball having a plurality of recessed dimples on the surface thereof, at least a portion of which have a cross-sectional profile including a base portion and a Gabriel's Horn portion. The base portion of the profile, 0≦x<x₀, is defined by a function selected from the group consisting of polynomial, posynomial, trigonometric, hyperbolic, and exponential functions. The Gabriel's Horn portion of the profile,

${x_{0} \leq x \leq \frac{d_{d}}{2}},$

is defined by an equation in the form of:

${{y(x)} = \frac{{C_{d}\left( {\frac{2}{d_{d}} - \frac{1}{x}} \right)}\left( \frac{d_{d}}{2} \right)}{\left( {{H\; F} - 1} \right)}},$

where C_(d) is the chord depth, d_(d) is the dimple diameter, and HF is the horn factor. The horn factor is defined as:

${{H\; F} = \frac{d_{d}}{d_{b}}},$

where d_(d) is the dimple diameter and d_(b) is the dimple base diameter.

BRIEF DESCRIPTION OF DRAWINGS

In the accompanying drawings, which form a part of the specification and are to be read in conjunction therewith, and which are given by way of illustration only, and thus are not meant to limit the present invention:

FIG. 1 shows a portion of a dimple cross-sectional profile according to one embodiment of the present invention;

FIG. 2 shows a portion of a dimple cross-sectional profile according to another embodiment of the present invention;

FIG. 3 shows a portion of a dimple cross-sectional profile according to another embodiment of the present invention; and

FIG. 4 shows a portion of a dimple cross-sectional profile according to another embodiment of the present invention.

DETAILED DESCRIPTION

Golf balls of the present invention include dimples having a cross-sectional profile partially defined by a Gabriel's Horn curve. Gabriel's Horn, also known as Torricelli's

Trumpet, is a curve defined by the Cartesian equation:

${{y(x)} = \frac{1}{x}},{x \geq 1},{x \leq {- 1.}}$

This equation is manipulated to provide the following equation, which defines the Gabriel's Horn portion of a dimple cross-sectional profile:

${{y(x)} = \frac{{C_{d}\left( {\frac{2}{d_{d}} - \frac{1}{x}} \right)}\left( \frac{d_{d}}{2} \right)}{\left( {{H\; F} - 1} \right)}},{x_{0} \leq x \leq \frac{d_{d}}{2}},$

where C_(d) is the chord depth, d_(d) is the dimple diameter, and HF is the horn factor.

The second derivative of the defining function of Gabriel's Horn is negative, indicating that the Gabriel's Horn portion of the dimple profile is defined by a concave down curve, shown below:

$- \frac{C_{d}d_{d}}{x^{3}\left( {{H\; F} - 1} \right)}$

where C_(d) is the chord depth, d_(d) is the dimple diameter, and HF is the horn factor.

The horn factor is defined as:

${{H\; F} = \frac{d_{d}}{d_{b}}},$

where d_(d) is the dimple diameter and d_(b) is the dimple base diameter. The horn factor, HF, can be any real number greater than 1. In a particular embodiment, HF is within a range having a lower limit of 1.3 or 1.5 and an upper limit of 4 or 15 or 30.

The remaining portion of the dimple cross-sectional profile, 0≦x<x₀, is referred to herein as the base portion of the dimple. In one embodiment, the base portion of the dimple is defined by the following equation:

y(x)=−C _(d),0≦x<x ₀

where C_(d) is the chord depth.

In another embodiment, the base portion of the dimple is defined by any simple plane curve selected from polynomial, posynomial, trigonometric, hyperbolic, and exponential functions.

The following should be taken into account:

-   -   1) the chord plane of the dimple represents y=0, and     -   2) the vertical axis in the center of the dimple represents x=0.

FIG. 1 illustrates a dimple profile resulting from a combination of a Gabriel's horn portion and a base portion, each being defined according to the respective equations above. The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface.

FIG. 2 illustrates a dimple profile resulting from a combination of a Gabriel's horn portion and a base portion, the Gabriel's horn portion being defined according to the Gabriel's horn equation above, and the base portion being defined by a polynomial function: y(x)=ax²+bx+c. The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface. The highest order of the polynomial will dictate the overall shape of the base curve and the constants a, b, and c are used to modify the curvature intensity of the base curve. While FIG. 2 illustrates a base portion defined by a 2^(nd) order polynomial, it should be understood that a polynomial of any order and containing any number terms may be used.

FIG. 3 illustrates a dimple profile resulting from a combination of a Gabriel's horn portion and a base portion, the Gabriel's horn portion being defined according to the Gabriel's horn equation above, and the base portion being defined by a trigonometric function: y(x)=a sin(x^(n)). The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface. While FIG. 3 illustrates a base portion defined by a sin function, it should be understood that any trigonometric or hyperbolic trigonometric function may be used.

FIG. 4 illustrates a dimple profile resulting from a combination of a Gabriel's horn portion and a base portion, the Gabriel's horn portion being defined according to the Gabriel's horn equation above, and the base portion being defined by an exponential function: y(x)=ce^(x) ^(n) . The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface. While FIG. 4 illustrates a base portion defined by a specific exponential function, it should be understood that any exponential function may be used.

Dimples according to the present invention preferably have a dimple diameter, d_(d), within a range having a lower limit of 0.005 inches or 0.020 inches or 0.090 inches or 0.100 inches or 0.115 inches or 0.125 inches and an upper limit of 0.185 inches or 0.200 inches or 0.225 inches or 0.250 inches or 0.300 inches.

Dimples according to the present invention preferably have a base diameter, d_(b), within a range having a lower limit of 0.003 inches or 0.010 inches or 0.030 inches or 0.050 inches or 0.080 inches and an upper limit 0.100 inches or 0.120 inches or 0.175 inches or 0.200 inches or 0.275 inches.

The chord depth, C_(d), of dimples of the present invention is typically within a range having a lower limit of 0.001 inches or 0.005 inches or 0.007 inches and an upper limit of 0.010 inches or 0.015 inches or 0.020 inches or 0.030 inches or 0.040 inches.

The dimple volume of dimples of the present invention is typically within a range having a lower limit of 2.673* 10⁻⁷ in³ or 3.184* 10⁻⁶ in³ or 2.303*10⁻⁵ in³ and an upper limit of 1.500*10⁻⁴ in³ or 1.676*10⁻⁴ in³ or 3.581*10⁻⁴ in³ or 1.000*10⁻³ in³ or 1.166*10⁻³ in³.

The volume ratio of the dimple, V₀ is the fractional ratio of the dimple volume divided by the volume of a cylinder defined by a diameter and chord depth similar to that of the dimple, and is defined by:

$V_{0} = \frac{V}{{\pi \left( \frac{d_{d}}{2} \right)}^{2}C_{d}}$

where V is dimple volume, C_(d) is the chord depth, and d_(d) is the dimple diameter. The volume ratio of dimples of the present invention is less than 1, and is typically within a range having a lower limit of 0.02 or 0.03 or 0.07 or 0.25 and an upper limit of 0.70 or 0.80 or 0.90.

The dimple profile dimensions preferably adhere to the Bell Ratio, BR, such that:

${B\; R} = {\frac{d_{d}}{d_{b}}*C_{d}}$ or B R = H F * C_(d)

where C_(d) is the chord depth, d_(d) is the dimple diameter, d_(b) is the dimple base diameter, and HF is the horn factor. For purposes of the present invention, the Bell Ratio is typically within a range having a lower limit of 0.01 or 0.02 and an upper limit of 0.03 or 0.07.

The tangential angle, θ_(T), at any point on the Gabriel's Horn portion of the profile is calculated as follows:

$\theta_{T} = {\frac{180}{\pi}{\tan^{- 1}\left( \frac{C_{d}*d_{d}}{2\left( {{H\; F} - 1} \right)x^{2}} \right)}}$

where C_(d) is the chord depth, d_(d) is the dimple diameter, and HF is the horn factor.

The chord angle, θ_(CHORD), is the tangential angle of the curve at the dimple perimeter, and is calculated as follows:

$\theta_{CHORD} = {\frac{180}{\pi}{\tan^{- 1}\left( \frac{C_{d}*d_{d}}{2\left( {{H\; F} - 1} \right)\left( \frac{d_{d}}{2} \right)^{2}} \right)}}$

where C_(d) is the chord depth, d_(d) is the dimple diameter, and HF is the horn factor.

Dimples of the present invention typically have an edge angle within a range having a lower limit of 3° or 5° and an upper limit of 50° or 70° or 80°. Such edge angles can produce a preferred equivalent edge angle, for a spherical dimple with like volume, within a range having a lower limit of 3° or 10° or 12° and an upper limit of 16° or 30° or 50°.

Dimples of the present invention typically have an angle relative to the chord plane of less than 90°, and typically within a range having a lower limit of 0.03° or 0.30° or 2° and an upper limit of 15° or 30° or 60° or 75°.

Additionally, dimples of the present invention may be characterized by the angle formed between the base portion of the dimple, 0≦x<x₀, and the Gabriel's Horn portion of the dimple,

${x_{0} \leq x \leq \frac{d_{d}}{2}},$

referred to herein as the Bell Angle. Dimples of the present invention preferably have a Bell Angle within a range having a lower limit of 0° or 90° and an upper limit of 150° or 180°.

The present invention is not limited by any particular dimple pattern. Examples of suitable dimple patterns include, but are not limited to, phyllotaxis-based patterns; polyhedron-based patterns; and patterns based on multiple copies of one or more irregular domain(s) as disclosed in U.S. Pat. No. 8,029,388, the entire disclosure of which is hereby incorporated herein by reference; and particularly dimple patterns suitable for packing dimples on seamless golf balls. Non-limiting examples of suitable dimple patterns are further disclosed in U.S. Pat. Nos. 7,927,234, 7,887,439, 7,503,856, 7,258,632, 7,179,178, 6,969,327, 6,702,696, 6,699,143, 6,533,684, 6,338,684, 5,842,937, 5,562,552, 5,575,477, 5,957,787, 5,249,804, 5,060,953, 4,960,283, and 4,925,193, and U.S. Patent Application Publication Nos. 2006/0025245, 2011/0021292, 2011/0165968, and 2011/0183778, the entire disclosures of which are hereby incorporated herein by reference. Non-limiting examples of seamless golf balls and methods of producing such are further disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529, the entire disclosures of which are hereby incorporated herein by reference.

In a particular embodiment, the dimple pattern provides for overall dimple coverage of 60% or greater, or 65% or greater, or 75% or greater, or 80% or greater, or 85% or greater, or 90% or greater.

Golf balls of the present invention typically have a dimple count within a limit having a lower limit of 250 and an upper limit of 350 or 400 or 450 or 500. In a particular embodiment, the dimple count is 252 or 272 or 302 or 312 or 320 or 328 or 332 or 336 or 340 or 352 or 360 or 362 or 364 or 372 or 376 or 384 or 390 or 392 or 432.

Preferably, at least 30%, or at least 50%, or at least 60%, or at least 80%, or at least 90%, or at least 95% of the total number of dimples have a cross-sectional profile partially defined by a Gabriel's Horn curve, with the remaining dimples, if any, having a cross-sectional profile based on any known dimple profile shape including, but not limited to, parabolic curves, ellipses, spherical curves, saucer-shapes, sine curves, truncated cones, flattened trapezoids, and catenary curves. Among the dimples having a cross-sectional profile defined by the present invention, the profile of one dimple may be the same as or different from the profile of another dimple. Similarly, among the remaining dimples, if any, having a known dimple profile shape, the profile of one dimple may be the same as or different from the profile of another dimple.

The present invention is not limited by any particular golf ball construction or any particular composition for forming the golf ball layers. For example, functionally weighted curves of the present invention can be used to form dimple profiles on one-piece, two-piece (i.e., a core and a cover), multi-layer (i.e., a core of one or more layers and a cover of one or more layers), and wound golf balls, having a variety of core structures, intermediate layers, covers, and coatings.

When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used.

All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted.

While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains. 

What is claimed is:
 1. A golf ball having a plurality of recessed dimples on the surface thereof, wherein at least a portion of the recessed dimples have a cross-sectional profile including a base portion, 0<x<x₀ , and a Gabriel's Horn portion, ${x_{0} \leq x \leq \frac{d_{d}}{2}},$ where d_(d) is the dimple diameter; wherein the base portion is defined by a function selected from the group consisting of polynomial, posynomial, trigonometric, hyperbolic, and exponential functions; and wherein the Gabriel's Horn portion is defined by an equation in the form of: ${{y(x)} = \frac{{C_{d}\left( {\frac{2}{d_{d}} - \frac{1}{x}} \right)}\left( \frac{d_{d}}{2} \right)}{\left( {{H\; F} - 1} \right)}},$ where C_(d) is the chord depth, d_(d) is the dimple diameter, and HF is the horn factor defined as: ${{H\; F} = \frac{d_{d}}{d_{b}}},$ where d_(d) is the dimple diameter and d_(b) is the dimple base diameter.
 2. The golf ball of claim 1, wherein the horn factor, HF, is from 1.3 to
 30. 3. The golf ball of claim 1, wherein the horn factor, HF, is from 1.3 to
 15. 4. The golf ball of claim 1, wherein the horn factor, HF, is from 1.5 to
 4. 5. The golf ball of claim 1, wherein the chord depth, C_(d), is from 0.001 inches to 0.040 inches.
 6. The golf ball of claim 1, wherein the chord depth, C_(d), is from 0.005 inches to 0.020 inches.
 7. The golf ball of claim 1, wherein the chord depth, C_(d), is from 0.007 inches to 0.015 inches.
 8. The golf ball of claim 1, wherein the dimple has a volume ratio of from 0.07 to 0.90.
 9. The golf ball of claim 1, wherein the dimple has a volume ratio of from 0.25 to 0.80. 